Additional work that is novel to this thesis pertains to the study of the phase \(\Phi \)  in quantum field theory. As discussed in the previous chapter, T. C. Wallstrom [1]} objected to the claim that Nelson's stochastic mechanics was, in fact, equivalent to conventional quantum mechanics. The argument, which we will discuss in more detail below, levied that reconstructions of quantum theory based on the real-valued variables \(\rho \)  and \(\Phi \)  tend to be problematic in that either the phase \(\Phi \)  is single valued, or if it is not, then the quantum state \(\Psi \)  is multi-valued, unless one postulates an additional ad hoc quantization condition. Below we discuss how this criticism is evaded in the ED approach to quantum scalar fields. It should also be noted that such an analysis appears to be entirely unique, as most consideration of this issue appears confined to the domain of particles in quantum mechanics.
